In the communication system, the Constant Amplitude Zero Auto-Correlation (CAZAC) sequence is a very important communication resource. The specific features are as follows:
The modulo of the amplitude is a constant value, for example, normalized to 1; and
Zero periodical-auto-correlation: except the maximum correlation with the sequence itself, the auto correlation with other cyclic shift of this sequence is zero.
The CAZAC sequence has the above features. Therefore, after Fourier transformation, the sequence in the frequency domain is also a CAZAC sequence. The sequence of this feature may be used as a reference signal for channel estimation in the communication.
For example, in a Single Carrier Frequency Division Multiple Access (SC-FDMA) system, within a symbol time, the elements of the CAZAC sequence are transmitted sequentially on multiple sub-carriers. If the receiver knows the sequence of the transmitted signals, the receiver may perform channel estimation by using the received signals. The transmitted signals have equal amplitudes on every sub-carrier on the frequency domain. Therefore, the receiver may estimate out the channel fading on each sub-carrier fairly. In addition, due to the constant amplitude feature of the CAZAC sequence on the time domain, the peak-to-average value of the transmitted waveform is relatively low, which facilitates transmitting.
In another example, the random access preamble signals in the SC-FDMA system may be made of CAZAC sequences. The preamble sequence of the random access signals may be modulated on the frequency domain sub-carrier, and transformed onto the time domain through Fourier transformation before being transmitted. In this way, through high auto correlation and cross correlation of the CAZAC sequence, little interference exists between the random access preamble signals of different cells and different users.
A CAZAC signal is manifested as a CAZAC signal on both the time domain and the frequency domain. Therefore, the CAZAC signals may also be modulated directly into signals on the time domain that occupies certain bandwidth before being transmitted.
The CAZAC sequence comes in many types. A common type is Zadoff-Chu sequence. Other types include: Generalized Chirplike Sequence (GCL) and Milewski sequence. Taking the Zadoff-Chu sequence as an example, the generation mode or expression of a Zadoff-Chu sequence is as follows:
                                          a                          r              ,              N                                ⁡                      (            k            )                          =                  {                                                                      exp                  ⁡                                      [                                                                  -                                                                              j                            ⁢                                                                                                                  ⁢                            2                            ⁢                                                          π                              ·                              r                                                                                N                                                                    ⁢                                              (                                                                              q                            ·                            k                                                    +                                                                                    k                              ·                                                              (                                                                  k                                  +                                  1                                                                )                                                                                      2                                                                          )                                                              ]                                                                                                                                                                                            N                          ⁢                                                                                                          ⁢                          is                          ⁢                                                                                                          ⁢                          an                          ⁢                                                                                                          ⁢                          odd                          ⁢                                                                                                          ⁢                          number                                                ,                                                                                                                                                                          k                          =                          0                                                ,                        1                        ,                        …                        ⁢                                                                                                  ,                                                  N                          -                          1                                                                                                                                                                                          exp                  ⁡                                      [                                                                  -                                                                              j                            ⁢                                                                                                                  ⁢                            2                            ⁢                                                          k                              ·                              r                                                                                N                                                                    ⁢                                              (                                                                              q                            ·                            k                                                    +                                                                                    k                              2                                                        2                                                                          )                                                              ]                                                                                                                                                                                            N                          ⁢                                                                                                          ⁢                          is                          ⁢                                                                                                          ⁢                          an                          ⁢                                                                                                          ⁢                          even                          ⁢                                                                                                          ⁢                          number                                                ,                                                                                                                                                                          k                          =                          0                                                ,                        1                        ,                        …                        ⁢                                                                                                  ,                                                  N                          -                          1                                                                                                                                                                            Formula        ⁢                                  ⁢                  (          1          )                    
wherein r is a parameter generated by the sequence and is relatively prime to N, and q is an integer. When the value of r varies, the sequence differs. r is named as a basic sequence index, and q corresponds to different cyclic shifts. That is, the r value determines the basic sequence, and the q value determines different cyclic shifts of the same basic sequence. The sequence generated by different cyclic shifts of a sequence is known as a cyclic shift sequence generated by the same basic sequence. For two different r values such as r=u, r=v, when (u−v) is relatively prime to N, the two sequences are highly cross-correlated. When N is a prime number, r=1, 2, . . . , N−1, and N−1 different CAZAC sequences are generated. Such sequences are highly cross-correlated. In the above example, when N is a prime number, the absolute value of cross correlation normalized between the two sequences is √{square root over (N)}. The conjugate of the Zadoff-Chu sequence is also a CAZAC sequence.
In a general cellular communication system, when a cell selects a sequence for modulation and transmission, another cell needs to select another sequence having the feature of low cross correlation. For example, in the case of using a Zadoff-Chu sequence, if N is a prime number, each cell selects a different r value, thus ensuring low cross correlation and low interference.
The modulated signals transmitted by a cell may also adopt the fragments of the old sequence or repeat cyclically, which also maintains the auto correlation and cross correlation features of the old sequence properly. Particularly, when the number of sub-carriers that bear the sequence in the cell is not a prime number, it is necessary to select the sequence whose length is equal to the prime number around the number of sub-carriers, and the desired sequences are obtained through segmentation or cyclic extension of the sequences before being transmitted. In the following description, the operations of segmentation or cyclic extension of the sequence are omitted.
When the signals of multiple sequences transmitted by different cells occupy the same time frequency resource, the sequences transmitted by cell A and cell B have the same length, as shown in FIG. 1. For example, two different Zadoff-Chu sequences whose length is a prime number N may be selected. When the basic sequence index of one sequence is different from that of the other, the two sequences are little correlated, and the transmitted signals of different cells are little mutual-interfering.
As shown in FIG. 2, when the signals of the modulated sequence occupy different time frequency resources, some users of cell A transmit sequence-modulated signals on the radio resource with bandwidth B1; meanwhile, some users of cell B transmit sequence-modulated signals on the radio resource with bandwidth B2, and the time frequency resources of the two parts overlap. In the system shown in FIG. 2, all cells have the same sub-carrier width. Within bandwidth B1, 36 sub-carriers exist. Within bandwidth B2, 144 sub-carriers exist. Because the sequence is mapped onto a sub-carrier, the length of the sub-carrier corresponds to the length of the sequence. Evidently, the two cells need to select sequences of different lengths respectively. In this case, the cross interference may be strong between the long sequence and the short sequence, and the sequence planning becomes relatively complex. In the example shown in FIG. 2, only sequences of two lengths exist. In practice, depending on the size of different radio resources occupied by a user's transmission, more sequences of different lengths may exist, and the complexity is higher.
The foregoing modulated signals of the sequences that occupy different time frequency resources occur frequently in the SC-FDMA system. Because the sequence serves as a reference signal and provides the channel estimation required by data demodulation, the sequence is transmitted along with the bandwidth resources of the data. The data bandwidth of the user may have different bandwidth values and locations at different times according to specific scheduling rules. Therefore, the sequence of the reference signal of each different cell occupies the time frequency resources in a way that is frequently changing, and the interference between cells is affected by the correlation of sequences of different lengths. To make matters worse, the system generally uses the shift correlation feature of sequences, obtains multiple code division quadrature sequences through different cyclic time shifts, and allocates them to different users. Therefore, once strong interference occurs between the sequences of two lengths, the users who use the sequences of the two lengths may interfere with each other strongly.
Nevertheless, the modes of the sequence occupying the time frequency resources are not limited to the foregoing examples. For example, sequences of different lengths may be modulated on the time domain at the same sampling frequency, which also brings the issue of correlation between the long sequence and the short sequence. Alternatively, the sequence may occupy the frequency domain sub-carriers at different sub-carrier intervals, or occupy the time sampling points at different time sampling intervals. In other words, the sequence is not modulated on all sub-carriers/sampling points, but modulated at regular intervals equivalent to a specific number of sub-carriers/sampling points.
To sum up, when the sequence occupies the time frequency resource in different modes, the interference among cells is relatively complex. Particularly, when sequences of different lengths exist, the sequences of each length need to be planned separately, and the interference among sequences with different length needs to be considered in a system with multiple cells.